Snap an animated rig to another static rig position while keeping the animation of the first one (MoCap, Kinect)
To understand your problem, let we simplify: suppose that rotating the left arm from T pose to A pose is happening with a 45 degrees rot on X axis arm bone; 90 degrees will take the arm vertical, along the body. If the animation data store a value of 90 starting from a T pose, the same animation data will take the arm inside the body if applied to an A pose rig.
So there are many ways to solve the problem. The simpliest is to set your character to a rest T pose, matching the Kinect rig rest position (as it is in the video tutorial).
If you really don't want that you will have to create an empty in the loc of the Kinect bone and child of it. Then you set a copy rot constraint to your CharacterBone targeting the empty.
Once the setup is established you set the Kinect rig in rest pose and rotate the empty until the two arm bones are perfectly aligned in their T pose, so that when the animation says 0 degrees you get a T pose, when it says 45 degrees you get A pose, when it says 90 degrees you get the arm along the body, as expected.
You will have to trim the empty on the other 2 axis of rotation also, and repeat the operation for all involved bones.